The parametric equation of a plane in space through $$\xvec_0=(x_0, y_0, z_0)$$ which contains two non-collinear vectors $$\uvec$$ and $$\vvec$$ is $$$ \xvec = \xvec_0 + \lambda\uvec+\mu\vvec,\qquad \lambda,\mu\in\R.$$$ This is also called the vector equation. $$\uvec$$ and $$\vvec$$ are non unique.